• Recent Problems

    Write 2014 with the first four prime numbers, with the aid of the operations addition, multiplication and exponentiation.
    Grades: 6th to 8th, 3rd to 5th
    Algebraic Thinking
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Gain familiarity with factors and multiples.
    Multiply and divide within 100.
    3.OA.C.7, 4.OA.B.4, 6.EE.A.1

    To the left, an 8 × 8 grid can be covered by one square (measuring 8 × 8), by four squares (measuring 4 × 4 each), or by ten squares (one 5 × 5, three 3 × 3, two 2 × 2, and four 1 × 1). 

    Find all values of n for which it is impossible to cover an 8 × 8 grid with n squares of integer side length.

    Grades: 3rd to 5th
    Measurement & Data
    Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
    3.MD.C.5a, 3.MD.C.5b, 3.MD.C.6

    Consider three six-sided dice A, B, and C, with the following numbers on their sides:

    A: 2, 2, 4, 4, 9, 9

    B: 1, 1, 6, 6, 8, 8

    C: 3, 3, 5, 5, 7, 7

    What is the probability that:

    ·     A produces a higher number than B?

    ·     B produces a higher number than C?

    ·     C produces a higher number than A?

    Can you find another set of face values for A, B, and C that yield the same properties? (Does such a set even exist?)

    Grades: 6th to 8th
    Stats & Probability
    Investigate chance processes and develop, use, and evaluate probability models.
    7.SP.C.5, 7.SP.C.7a

    A 40‑inch straightedge (without markings) is divided into four pieces. The length of each piece is an integer number of inches. These four pieces, when used in tandem, can be used to measure any integer length from 1 to 40 inches.

    What are the lengths of the pieces?


    The rectangle shown consists of eight squares. The length of each side of each square is 1 unit. The length of the shortest path from A to C using the lines shown is 6 units. 

    How many different six-unit paths are there from A to C?

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